Geometry & Topology

The Gromov width of $4$–dimensional tori

Janko Latschev, Dusa McDuff, and Felix Schlenk

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Abstract

Let ω be any linear symplectic form on the 4–torus T4. We show that in all cases (T4,ω) can be fully filled by one symplectic ball. If (T4,ω) is not symplectomorphic to a product T2(μ)×T2(μ) of equal sized factors, then it can also be fully filled by any finite collection of balls provided only that their total volume is less than that of (T4,ω).

Article information

Source
Geom. Topol., Volume 17, Number 5 (2013), 2813-2853.

Dates
Received: 27 September 2012
Accepted: 13 June 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732688

Digital Object Identifier
doi:10.2140/gt.2013.17.2813

Mathematical Reviews number (MathSciNet)
MR3190299

Zentralblatt MATH identifier
1277.57024

Subjects
Primary: 57R17: Symplectic and contact topology 57R40: Embeddings
Secondary: 32J27: Compact Kähler manifolds: generalizations, classification

Keywords
Gromov width symplectic embeddings symplectic packing symplectic filling tori

Citation

Latschev, Janko; McDuff, Dusa; Schlenk, Felix. The Gromov width of $4$–dimensional tori. Geom. Topol. 17 (2013), no. 5, 2813--2853. doi:10.2140/gt.2013.17.2813. https://projecteuclid.org/euclid.gt/1513732688


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